For stochastic models, using Monte Carlo simulation methods can obtain the distribution results of LCOE, which provides the possibility for quantitative analysis of uncertainty. For risk averse investors, they will choose options with low uncertainty, even if their LCOE value is relatively high. Uncertainty premium refers to the cost paid to reduce uncertainty and is a method of monetizing investment risk. In order to quantitatively evaluate various possibilities, a risk avoidance model is used here to calculate the deterministic equivalent of LCOE for different energy storage systems, that is, the deterministic equivalent of quantitative uncertainty. Deterministic equivalence is a function of decision-makers’ risk aversion, indicating that they are more concerned about the distribution of LCOE with uncertainty compared to fixed LCOE values. Because most investors are risk averse, the certainty equivalent is generally higher than the expected cost. If uncertainty can be eliminated, risk averse decision-makers are willing to pay higher expected costs.
In order to calculate the LCOE values of different energy storage systems, it is necessary to measure uncertainty, also known as Risk Premium (RP), and the equation provides the calculation method. Risk premium RP is a function of risk aversion, LCOE is the value obtained from each run in Monte Carlo simulation analysis, and N is the number of runs, γ It is the risk avoidance coefficient, which can be changed by γ The value represents the risk aversion level of investment decision-makers, γ The larger the value, the higher the degree of risk aversion. Here, it is assumed that the value of the risk aversion coefficient is 2. After obtaining the risk overflow value, the deterministic equivalent 𝐶𝑒 q of each energy storage system LCOE can be obtained, as shown in the formula. A higher level of risk aversion leads to a higher risk premium, which corresponds to a higher level of certainty equivalence.
| Two-tank | Concrete | PCM-L | PCM-M | PCM-H | PCM-T | C-PCM2 | |
| Expected value | 0.2485 | 0.2001 | 0.1852 | 0.1850 | 0.1947 | 0.1897 | 0.1756 |
| Uncertainty premium RP | 0.0135 | 0.0108 | 0.0102 | 0.0101 | 0.0111 | 0.0103 | 0.0096 |
| Deterministic Equivalence 𝐶𝑒q | 0.2620 | 0.2109 | 0.1954 | 0.1951 | 0.2058 | 0.2000 | 0.1852 |
Tables 1 and 2 provide estimates of the uncertainty premium and certainty equivalent LCOE for different energy storage systems, reflecting the impact of system LCOE variability on risk averse investment decision-makers. These results assume that the decision-maker’s risk aversion is constant. The expected value is the average LCOE of different energy storage systems in a stochastic model, and the uncertainty premium is the equivalent additional cost associated with LCOE uncertainty. The wider the distribution of LCOE, the higher the uncertainty premium. Deterministic equivalence is the sum of expected value and uncertainty premium, which is the cost that decision-makers pay for ignoring uncertainty.
| Two-tank | Concrete | PCM-L | PCM-M | PCM-H | PCM-T | C-PCM2 | |
| Expected value | 0.1758 | 0.1415 | 0.1311 | 0.1309 | 0.1378 | 0.1342 | 0.1242 |
| Uncertainty premium RP | 0.0113 | 0.0090 | 0.0085 | 0.0084 | 0.0092 | 0.0085 | 0.0079 |
| Deterministic Equivalence 𝐶𝑒q | 0.1871 | 0.1505 | 0.1396 | 0.1393 | 0.1470 | 0.1427 | 0.1321 |
From the perspective of the expected value and uncertainty premium of different energy storage systems, the value of the sensible latent heat combination energy storage system is the smallest. In the Blue Map scenario, its expected value and uncertainty premium are 0.1756 $/kWh and 0.0096 $/kWh, respectively, while in the Roadmap scenario, the expected value and uncertainty premium are 0.1242 $/kWh and 0.0079 $/kWh, respectively. In both scenarios, the expected value and uncertainty premium of the dual tank molten salt energy storage system are the highest, indicating that the sensible latent heat combined energy storage system is the most economical alternative among all options, with its deterministic equivalent reduced by 29.31% and 29.40%, respectively, compared to the dual tank molten salt energy storage system.